adaptive model predictive control

In the following link (or above picture) in the controlled system, why are the initial inputs and outputs are subtracted from system inputs/outputs and the resulting signals then delayed? I have indicated these parts in a red rectangle.

http://nl.mathworks.com/help/mpc/ug/adaptive-mpc-control-of-nonlinear-chemical-reactor-using-online-model-estimation.html

Answer 1

[Arkadiy Turevskiy]

The intitial values are substracted to remove the offset from the data. The delay block resamples continuous signals coming from the plant model, as the estimator requires discrete-time signals sampled at Ts. You could use Rate Transition block instead.

Hope this helps.

[E U]

Thanks Arkadiy for your answer. Still, I wonder the question that I asked in the attached picture. I will be happy for your feedback on my question.